Question

identify the symbols used for each of the following: (a) sample standard deviation; (b) population standard deviation; (c) sample variance; (d) population variance. if sample data consist of weights measured in grams, what units are used for these statistics and parameters?a. the symbol for sample standard deviation isb. the symbol for population standard deviation isc. the symbol for sample variance isd. the symbol for population variance is

Explanation:

Step1: Recall symbols for sample standard deviation

In statistics, the symbol for sample standard deviation is \(s\).

Step2: Recall symbols for population standard deviation

The symbol for population standard deviation is \(\sigma\).

Step3: Recall symbols for sample variance

Since variance is the square of standard deviation, the symbol for sample variance is \(s^{2}\).

Step4: Recall symbols for population variance

The symbol for population variance is \(\sigma^{2}\).

Step5: Determine units

• For standard deviation (both sample and population): Since standard deviation is the square - root of variance and if the original data (weights) are in grams, the units of standard deviation are grams.
• For variance (both sample and population): Since variance is the square of the standard deviation (and the standard deviation has units of grams), the units of variance are grams squared (\(g^{2}\)).

Answer:

a. \(s\)
b. \(\sigma\)
c. \(s^{2}\)
d. \(\sigma^{2}\)
Units:

• Standard deviation (sample and population): grams (\(g\))
• Variance (sample and population): grams squared (\(g^{2}\))